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NCERT Class XII Mathematics Chapter - - Solutions

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Question 31 - 33: Find the cartesian equation of the following planes:
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Question : 33 of 78
Marks: +1, -0
r⃗⋅(2i^+2j^−4k^)=1\vec{r} \cdot (\hat{2i}+\hat{2j}-\hat{4k})=1
Solution:  
We have : r⃗⋅(2i^+2j^−4k^)=1\vec{r} \cdot (\hat{2i}+\hat{2j}-\hat{4k})=1
⇒(xi^+yj^+zk^)⋅(2i^+2j^−4k^)=1\Rightarrow (\hat{xi}+\hat{yj}+\hat{zk}) \cdot (\hat{2i}+\hat{2j}-\hat{4k})=1
⇒ 2x + 3y – 4z = 1, which is the required cartesian equation.
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